Barrier function method and correction algorithms for improper convex programming problems

2008 ◽  
Vol 263 (S2) ◽  
pp. 120-134 ◽  
Author(s):  
V. D. Skarin
Keyword(s):  
Convex Programming ◽  
Barrier Function ◽  
Function Method

scholarly journals DEVELOPMENT OF SOFTWARE FOR SOLVING PROBLEMS WITH THE PENALTY FUNCTION METHOD

2020 ◽  
Vol 7 (1) ◽  
pp. 84-87
Author(s):  
Galina E. Egorova ◽  
Tatyana S. Zaitseva
Keyword(s):  
Nonlinear Programming ◽  
Convex Programming ◽  
Penalty Function ◽  
Function Method ◽  
Theoretical Research ◽  
Penalty Function Method ◽  
Indirect Methods ◽  
Economic Problems ◽  
Definition Of

The penalty function method is one of the most popular and universal methods of convex programming and belongs to the group of indirect methods for solving nonlinear programming problems. Thе article discusses the algorithm for solving problems by the penalty function method, provides an example of a solution. A complete definition of the concepts used in the theoretical material of the method, and examples of its application are also given. It is worth noting that these methods are widely used to solve technical and economic problems. Also they are quite often used both in theoretical research and in the development of algorithms. The result of the work is the development of software for solving problems using the penalty function method.

scholarly journals A modified barrier function method with improved rate of convergence for degenerate problems

1980 ◽  
Vol 21 (3) ◽  
pp. 305-329 ◽  
Author(s):  
Krisorn Jittorntrum ◽  
M. R. Osborne
Keyword(s):  
Rate Of Convergence ◽  
Barrier Function ◽  
Function Method ◽  
Degenerate Problems ◽  
Scaling Properties ◽  
Classical Algorithm ◽  
Nondegenerate Case ◽  
Accelerate Convergence

AbstractIn a previous paper the authors have shown that the classical barrier function has anO(r) rate of convergence unless the problem is degenerate when it reducesO(r½). In this paper a modified barrier function algorithm is suggested which does not suffer from this problem. It turns out to have superior scaling properties which make it preferable to the classical algorithm, even in the nondegenerate case, if extrapolation is to be used to accelerate convergence.

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